I worked in Singapore last week, doing our periodic moderation activity with Informatics. I took my bike along, but had very little time to get out unfortunately. Singapore isn't too bad to cycle in (and there are quite a lot of cyclists around). In the city the roads are mostly one way, which is a pain as a cyclist. There is often a bus/taxi lane on the left which isn't too bad to use to cycle, although it often turns into a left/straight ahead lane at the junctions, which leaves you with the quandary of how position yourself safely. As some motorists do not indicate when in the lane, its often difficult to predict their behaviour. Many cyclists use the pavements, there are a few do not cycle signs, but mostly I think using the pavements is accepted. There are also a lot of mopeds of one sort or another, so motorists are typically aware of two wheel traffic. Outside the city there are often cycle lanes on pavements, in the residential areas. So, on the whole not too bad.
Folding bikes are allowed on the MTR, but only after 8pm or during the weekends. The MTR is a great public transport system, you don't realise how fast it is until you cycle the same distances.
So Singapore suffers from the same problems as many countries, too many fast uncrossable roads, too many large 4*4s and other fantasy vehicles. However its somewhat easier because of the good public transport infrastructure, and the limits on the number of vehicle licences.